This “Sign in as Different User” menu item is very useful when testing applications, but it can lead to problems especially when opening documents, say in Microsoft Word. So, it may be for these reasons that the option has been removed in SharePoint 2013.
You can add the menu item back in, but I would suggest only doing this on test or development SharePoint servers. To do this, repeat this edit on all servers in your SharePoint farm:
- Locate the file \15\TEMPLATE\CONTROLTEMPLATES\Welcome.ascx and open in a text editor.
- Add the following element before the existing element with the id of “ID_RequestAccess”:
- Save the file.